In a tweet, Alexandria police said, "Suspect is in custody and not a threat. PIO will be onscene shortly to share updates".
News agency Reuters quoted Republican lawmaker Mo Brooks as saying that Mr Scalise was shot in the hip. Besides, two law enforcement officers and one Congressional staffer were also injured.
The shooting took place at the annual game between lawmakers. There were 20 to 25 members of team at the practice session when the gunfire started, he said.
White House press secretary Sean Spicer tweeted to say US President Donald Trump and First Lady Melania Trump have been briefed about the attack.
President Trump issued a statement saying he and Vice President Mike Pence were "deeply saddened" by the shooting at.
"The Vice President and I are aware of the shooting incident in Virginia and are monitoring developments closely. We are deeply saddened by this tragedy. Our thoughts and prayers are with the members of Congress, their staffs, Capitol Police, first responders, and all others affected," President Trump said.
(With inputs from agencies)